Online First
Two Families of $n$-Rectangle Nonconforming Finite Elements for Sixth-Order Elliptic Equations
Xianlin Jin and Shuonan Wu

J. Comp. Math. DOI: 10.4208/jcm.2309-m2023-0052

Publication Date : 2023-12-25

  • Abstract

In this paper, we propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of the new finite element spaces are established. A new mechanism, called the exchange of sub-rectangles, for investigating the weak continuities of the proposed elements is discovered. With the help of some conforming relatives for the $H^3$ problems, we establish the quasi-optimal error estimate for the triharmonic equation in the broken $H^3$ norm of any dimension. The theoretical results are validated further by the numerical tests in both 2D and 3D situations.

  • Copyright

COPYRIGHT: © Global Science Press